interlockingring

Interlocking rings are a class of links formed by closed loops that are connected in such a way that removing or separating them without cutting or deforming at least one ring is impossible. The fundamental example is two rings interlocked once, known in knot theory as the Hopf link, which has a linking number of ±1.

With three rings, several configurations exist, including chain-like links and Borromean rings. The Borromean rings are a Brunnian link in which the three rings are collectively linked but removing any one ring liberates the other two, and no two rings are directly linked.

In practical use, interlocking rings appear in jewelry, decorative motifs, chainmail, and mechanical puzzles designed to challenge separation. They also feature in art and design as symbolic motifs such as unity or eternity.

From a mathematical perspective, interlocking rings are studied as links in three-dimensional space. Invariants such as the linking number distinguish linked pairs, while more complex links require additional tools from knot theory.

Manufacture may involve welding or soldering metal rings, forging, or casting, with plastic and glass versions also produced for decorative purposes. Interlocking rings thus span both practical applications and theoretical study, illustrating fundamental ideas about how simple loops can form stable, inseparable structures.